compound inequality

[blackempress]

can you please tell me how to work out these questions

-1 less than or equal to sign 2x-5 divided by 6 less than or equal to sign 1


and


|5 - x | less than or equal to sign 3

 

[wjm11]

-1 less than or equal to sign 2x-5 divided by 6 less than or equal to sign 1

Here is a similar example:

-4 < (7x + 2)/2 < 8

Our goal is to get x by itself. The first step is to get rid of the 2 in the denominator. We achieve this by multiplying everything by 2:

(2)(-4) < (2)(7x + 2)/2 < (2)(8)
-8 < 7x + 2 < 16

Now we want to get rid of the 2 in the “x + 2”, so we subtract 2 from everything:

-8 - 2 < 7x + 2 - 2 < 16 –2
-10 < 7x < 14

Our last step is to divide everything by 7:

-10/7 < 7x/7 < 14/7
-10/7 < x < 2

That’s it. “x” is between –10/7 and +2.

 

[stapel]

can you please tell me how to work out these questions

|5 - x | less than or equal to sign 3

To learn how to set up and solve absolute-value inequalities, try here. :wink: